I am a little torn on this. On one hand, I believe they are different and yet on the other I say not. Project managers are in charge of obtaining the end, desired result. This is alike for both professions but differs when considering the end result. Clinical project manager is typically only involved with medical settings. This includes ensuring those participating is following or updating the protocols and procedures as required by the institution they work for. An overall project manager is typically involved with the constraints of the community or multiple groups of people across different organizations.
Although they have similar goals in mind, I would consider a Clinical Project Manager a branch or division of a Project Manager.